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1.

図書

図書
Julius S. Bendat
出版情報: New York : Wiley, c1998  xiii, 474 p. ; 24 cm
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Linear Systems, Random Data
Zero-Memory Nonlinear Systems
Direct and Reverse MI/SO
Techniques for Analysis and Identification of Nonlinear Systems
Parallel Linear and Nonlinear Systems
Determination of Physical Parameters with Memory in Nonlinear Systems
Nonlinear System Response Properties of a Naval Frigate from Measured Ocean Engineering Data
Nonlinear System Response Properties of a Naval Barge from Measured Ocean Engineering Data
Bilinear and Trilinear Systems
Input Output Relations for Bilinear and Trilinear Systems
References
Index
Glossary of Symbols
Linear Systems, Random Data
Zero-Memory Nonlinear Systems
Direct and Reverse MI/SO
2.

図書

図書
J. Bourgain
出版情報: Providence, RI : American Mathematical Society, c1999  viii, 182 p. ; 26 cm
シリーズ名: Colloquium publications / American Mathematical Society ; v. 46
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Introduction and summary
An overview of results on the Cauchy problem for NLS
Further comments 3D $H^1$-critical defocusing NLS Global wellposedness below energy norm
Nonlinear Schrodinger equation with periodic boundary conditions
Growth of Sobolev norms in linear
Schrodinger equations with smooth time dependent potential
Zakharov systems
References
Index
Introduction and summary
An overview of results on the Cauchy problem for NLS
Further comments 3D $H^1$-critical defocusing NLS Global wellposedness below energy norm
3.

図書

図書
I.I. Vorovich ; English edition edited by L.P. Lebedev ; translated by Michael Grinfeld
出版情報: New York : Springer, c1999  xvi, 388 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 133
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4.

図書

図書
Thierry Aubin
出版情報: Berlin : Springer-Verlag, 1998  xvii, 395 p. ; 25 cm
シリーズ名: Springer monographs in mathematics
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5.

図書

図書
by Anatoliy K. Prykarpatsky and Ihor V. Mykytiuk
出版情報: Dordrecht : Kluwer Academic Press, c1998  553 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 443
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Preface
Background Notations
Dynamical systems with homogeneous configuration spaces / 1:
Dynamical systems with symmetries
Poisson structures / 1.1:
Lie group actions on manifolds / 1.2:
Symplectic structures on coadjoint representation orbits / 1.3:
Hamiltonian group actions / 1.4:
Invariant Hamiltonian systems with homogeneous configuration spaces / 1.5:
The existence of a maximal involutive set of functions on the orbits of semi-simple elements of a semi-simple Lie algebra / 2:
The algebra of invariant polynomials on a semi-simple Lie algebra / 2.1:
Semi-simple element orbits / 2.2:
Maximal involutive sets of functions on semi-simple elements orbits / 2.3:
The integrability criterion and spherical pairs of Lie groups / 3:
Criterion of integrability / 3.1:
Spherical pairs of complex Lie groups / 3.2:
Interpolation property of spherical pairs of compact Lie groups / 4:
Properties of spherical pairs of compact Lie algebras / 4.1:
Points in general position / 4.2:
Spherical pairs of classical simple Lie groups / 5:
Preliminary remarks / 5.1:
Involutions of simple Lie algebras / 5.2:
Spherical pairs of classical Lie algebras / 5.3:
Classification of spherical pairs of the exceptional simple Lie algebras / 6:
Classification of spherical pairs of semi-simple Lie groups / 7:
Spherical pairs of semi-simple Lie algebras / 7.1:
Geometric quantization and integrable dynamical systems
Connections on line bundles
Line bundles
Equivalence classes of line bundles
Connections
The integrality condition
Hermitian structures
Equivalence classes of line bundles with connections / 1.6:
Holomorphic line bundles / 1.7:
Derivations / 1.8:
Tensor products, square roots and invariant Hermitian structures / 1.9:
Parallel transport on a line bundle with a connection / 1.10:
Parallel transport and derivations / 1.11:
Flat partial connections
Flat F-connections
Maps of line bundles
Line bundles of differential forms
Geometric quantization
Polarizations
Geometric quantization and reduction
Introduction
Hamiltonian reduction
Quantization / 4.3:
Examples: geometric quantization of the oscillator type Hamiltonian systems
Geometric quantization of the generalized n-dimensional harmonic oscillator
Geometric quantization of geodesic flow on a sphere
Geometric quantization of the multidimensional Kepler problem
Geometric quantization of the MIC-Kepler problem / 5.4:
Structures on manifolds and algebraic integrability of dynamical systems
Poisson structures and dynamical systems with symmetries
Preliminary notes
Poisson structures on manifolds
Casimir functions and involution
Casimir functions associated with classical expansions of semi-simple Lie algebras
Alder-Kostant-Symes and Mishchenko-Fomenko theorems
The reduction method and Poisson structures on dual spaces of semi-direct sums of Lie algebras
The mapping canonicity of symplectic structures
Momentum mapping
Poisson structures on dual spaces of semi-direct sums of Lie algebras
Canonical mappings / 2.4:
Nonlinear Neumann type dynamical systems as integrable flows on coadjoint orbits of Lie groups
The Neumann problem
The Lie-Poisson bracket associated with the ad-semidirect sum of Lie algebras
The canonical symplectic structure on T(S[superscript n-1]) and its diffeomorphisms / 3.3:
An involutive system of integrals for the Neumann dynamical system on the sphere S[superscript n-1] / 3.4:
Generalized Neumann-Bogoliubov dynamical systems / 3.5:
Abelian integrals, integrable dynamical systems, and their Lax type representations
The Neumann-Rosochatius-Bogoliubov Hamiltonian system
Conservation laws
Lax type representation
Dual momentum mappings and their applications
Preliminaries
Dualities
The Neumann-Rosochatius system
The Lie algebraic setting of Benney-Kaup dynamical systems and associated via Moser Neumann-Bogoliubov oscillatory flows
The Novikov-Lax finite-dimensional invariant reductions on nonlocal submanifolds / 6.1:
The Moser map and its associated dual moment maps into loop Lie algebras / 6.3:
The finite-dimensional Moser type of reduction of modified Boussinesq and super-Korteweg-de Vries Hamiltonian systems via the gradient-holonomic algorithm and dual moment maps
The Moser type of finite-dimensional reduction of a Boussinesq hydrodynamic system and its Lie-algebraic integrability / 7.2:
The Neumann type of oscillatory super-Hamiltonian systems on the sphere S[superscript N] and their Lie algebraic super-integrability / 7.3:
Lax-type of flows on Grassmann manifolds and dual momentum mappings / 8:
Symplectic structures on loop Grassmann manifolds / 8.1:
An intrinsic loop Grassmannian structure and dual momentum mappings / 8.3:
On the geometric structure of integrable flows in Grassmann manifolds / 9:
Centrally extended symplectic structures and integrable flows on the loop Grassmann manifolds / 9.1:
Algebraic methods of quantum statistical mechanics and their applications
Current algebra representation formalism in nonrelativistic quantum mechanics
The current algebra in nonrelativistic quantum mechanics
Current algebra representations
Bogoliubov-Araki generating functional
Lie current algebra, Hamiltonian operator, and Bogoliubov functional equations
Hamiltonian operator
Gibbs states and the Kubo-Martin-Schwinger conditions
Stable states and the KMS condition
Functional-operator representations of the current Lie algebra
The Bogoliubov-Bloch functional equation / 2.5:
The reconstruction via Araki of the Hamiltonian operator and the Bogoluibov functional equation / 2.6:
Functional-operator solutions of the Bogoliubov functional equations / 2.7:
A generalized Virasoro algebra / 2.8:
The secondary quantization method and the spectrum of quantum excitations of a nonlinear Schrodinger type dynamical system
Preliminary notions
The second quantization representation
A generalized nonlinear Schrodinger type quantum dynamical system
The quantum inverse spectral transform method
The scattering operator
Eigenvalue states of the nonlinear Schrodinger type model / 3.6:
Quantum excitations of a bose gas with a positive momentum / 3.7:
Unitary representations of the generalized Virasoro algebra
Verma modules over the generalized Virasoro current algebra
Unitary irreducible modules with highest weight
Algebraic and differential geometric aspects of the integrability of nonlinear dynamical systems on infinite-dimensional functional manifolds
The current Lie algebra on S[superscript 1] and its functional representations
Basic notations
Associated cohomology complexes and their properties
Differential geometry analysis on real jet manifolds
Differential geometry analysis on jet supermanifolds
Euler variational derivative, external differential and tensors on infinite-dimensional functional spaces
Implectic operators and Poisson structures
Dynamical systems and bi-Hamiltonicity
The equivalence of dynamical systems as the Backlund transformation
The current Lie algebra on a cycle as a symmetry subalgebra of compatibly bi-Hamiltonian nonlinear dynamical systems on an axis
The Hamiltonicity of nonlinear dynamical systems on infinite-dimensional functional manifolds
A Lie-algebraic algorithm for investigating integrability
The gradient holonomic algorithm and Lax type representation
An adjoint Lax type equation and conservation laws
Lax type representation: differential algebraic approach
Lax type representation: geometric approach
Lagrangian and Hamiltonian formalisms for reduced infinite-dimensional dynamical systems with symmetries
General setting
Lagrangian reduction
Symplectic analysis and Hamiltonian fields
Discrete dynamical systems. One generalization
Non-isospectrally integrable dynamical systems: the generalized asymptotic structure of conservation laws
A nonstandard reduction problem
Lagrangian and Hamiltonian analysis of dynamical systems on functional manifolds. The Poisson-Dirac bracket / 3.8:
Conclusions / 3.9:
The algebraic structure of the gradient-holonomic algorithm for Lax type integrable nonlinear dynamical systems
Algebraic structure of the Lax type integrable dynamical system
The periodic problem and canonical variational relationships
The spectral gradient structure of Lax integrable many-dimensional nonlinear dynamical systems on operator manifolds / 4.4:
The integrability of Lie-invariant geometric objects generated by ideals in the Grassmann algebra
An effective Maurer-Cartan one-form construction
General structure of integrable one-forms augmenting the two-forms associated with a closed ideal in the Grassmann algebra
Cartan's invariant geometric object structure of the gradient-holonomic algorithm for Lax integrable nonlinear dynamical systems in partial derivatives
A loop algebra and the Yang-Baxter structure / 5.5:
The transfer matrix properties / 5.6:
The algebraic structure of the gradient-holonomic algorithm for the Lax-type nonlinear dynamical systems: the reduction via Dirac and the canonical quantization procedure
The generalized R-structure hierarchy
The Dirac quantization procedure for Moser induced finite-dimensional Neumann type Hamiltonian systems
The scalar and operator integrable Hamiltonian systems via the algebraic gradient-holonomic algorithm / 6.4:
Concluding remarks / 6.5:
Hamiltonian structures of hydrodynamical Benny type dynamical systems and their associated Boltzmann-Vlasov kinetic equations on an axis
The Boltzmann equation and an associated moment problem
A nonlinear completely integrable Schrodinger type dynamical system approximation
The complete integrability of a Benney type hydrodynamical system associated with a Boltzmann-Vlasov equation / 7.4:
Conclusion / 7.5:
Appendix
Basic definitions, examples / .1:
The tangent Lie algebra / .2:
Lie subgroups / .3:
Lie algebras / .4:
Cartan subalgebras / .5:
Semi-simple complex Lie algebras / .6:
References
Preface
Background Notations
Dynamical systems with homogeneous configuration spaces / 1:
6.

図書

図書
Aditya Kumar, Prodromos Daoutidis
出版情報: Boca Raton : Chapman & Hall/CRC, c1999  168 p. ; 24 cm
シリーズ名: Research notes in mathematics ; 397
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7.

図書

図書
Catherine Sulem, Pierre-Louis Sulem
出版情報: New York ; Tokyo : Springer, c1999  xvi, 350 p. ; 24 cm
シリーズ名: Applied mathematical sciences ; v. 139
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8.

図書

図書
Roger Temam
出版情報: New York : Springer, c1997  xxi, 648 p. ; 25 cm
シリーズ名: Applied mathematical sciences ; v. 68
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9.

図書

図書
Andreas Knauf, Yakov G. Sinai ; with a contribution by Viviane Baladi
出版情報: Basel : Birkhäuser Verlag, c1997  vi, 98 p. ; 24 cm
シリーズ名: DMV seminar ; Bd. 27
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10.

図書

図書
J.M. Dixon, J.A. Tuszyński, P.A. Clarkson
出版情報: New York : Oxford University Press, c1997  xv, 608 p.
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Premable
Introductory concepts / 1:
Phase transitions and criticality / 2:
Elementary excitations in solids / 3:
Quantum field theory background / 4:
The method of coherent structures (MCS) / 5:
The physical application of MCS / 6:
Mathematical methods and results / 7:
Concusions / 8:
appendices
Premable
Introductory concepts / 1:
Phase transitions and criticality / 2:
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